071. Stem-and-Leaf Plots

Learning Intentions

  • Interpret a stem-and-leaf plot
  • represent data in a stem-and-leaf plot

Pre-requisite Summary

  • Understand that numerical data can be organised to make patterns easier to see
  • Be able to order a set of whole numbers from smallest to largest
  • Understand place value, especially tens and ones
  • Know that a data display should show each value clearly and accurately
  • Be able to Identify the smallest and largest values in a data set
  • Understand that repeated values can occur in a data set

Worked Examples

Worked Example 1

A stem-and-leaf plot is shown below:

a) List the data values represented.

b) State the smallest and largest values.

c) How many data values are there?

Worked Example 2

A stem-and-leaf plot is shown below:

a) Interpret the plot by listing the data values.

b) State how many values are in the teens.

c) State the mode.

Worked Example 3

Represent the following data in a stem-and-leaf plot:

Worked Example 4

Represent the following data in a stem-and-leaf plot:

Worked Example 5

A stem-and-leaf plot is shown below:

a) Interpret the plot by writing the ordered data.

b) State the median.

c) State the range.

Worked Example 6

Represent the following data in a stem-and-leaf plot and then interpret it:

a) Draw the plot.

b) Identify the mode.

c) State the number of data values.

Problems

Problem 1

A stem-and-leaf plot is shown below:

a) List the data values represented.

b) State the smallest and largest values.

c) How many data values are there?

Problem 2

A stem-and-leaf plot is shown below:

a) Interpret the plot by listing the data values.

b) State how many values are less than .

c) State the mode.

Problem 3

Represent the following data in a stem-and-leaf plot:

071.p3.excalidraw.dark.svg

Problem 4

Represent the following data in a stem-and-leaf plot:

071.p4.excalidraw.dark.svg

Problem 5

A stem-and-leaf plot is shown below:

a) Interpret the plot by writing the ordered data.

b) State the median.

c) State the range.

071.p5.excalidraw.dark.svg

Problem 6

Represent the following data in a stem-and-leaf plot and then interpret it:

a) Draw the plot.

b) Identify the mode.

c) State the number of data values.

071.p6.excalidraw.dark.svg

Exercises

Understanding and Fluency

Exercise 1.

Interpret the stem-and-leaf plot:

a) List the data values.

b) State the smallest value.

c) State the largest value.

071.e1.excalidraw.dark.svg

Exercise 2.

Interpret the stem-and-leaf plot:

a) List the data values.

b) How many values are shown?

c) State the mode.

071.e2.excalidraw.dark.svg

Exercise 3.

Represent the data in a stem-and-leaf plot:

a)

b)

071.e3.excalidraw.dark.svg

Exercise 4.

Represent the data in a stem-and-leaf plot:

a)

b)

071.e4.excalidraw.dark.svg

Exercise 5.

Interpret the stem-and-leaf plot:

071.e5.excalidraw.dark.svg

a) Write the data in order.

b) State the median.

c) State the range.

071.e5.excalidraw.dark.svg

Exercise 6.

Interpret the stem-and-leaf plot:

a) Write the data in order.

b) State the mode.

c) State the number of data values.

071.e6.excalidraw.dark.svg

Exercise 7.

Represent the data in a stem-and-leaf plot, then answer the questions:

a)

b) State the mode.

c) State the largest value.

071.e7.excalidraw.dark.svg

Exercise 8.

Represent the data in a stem-and-leaf plot, then answer the questions:

a)

b) State the median.

c) State the range.

071.e8.excalidraw.dark.svg

Reasoning

Exercise 9.

Explain why the leaves in each row of a stem-and-leaf plot should be written in ascending order.

Exercise 10.

A student reads the row

as . Explain the mistake.

Exercise 11.

Explain why a stem-and-leaf plot is useful for showing the actual data values.

Exercise 12.

A student places the number in the row . Explain why this is incorrect.

Problem-solving

Exercise 13.

The test scores are .

a) Draw a stem-and-leaf plot.

b) State the mode.

c) State the range.

071.e13.excalidraw.dark.svg

Exercise 14.

The numbers of books read are .

a) Draw a stem-and-leaf plot.

b) State the median.

c) State how many values are in the teens.

071.e14.excalidraw.dark.svg

Exercise 15.

The daily temperatures are .

a) Draw a stem-and-leaf plot.

b) State the mode.

c) State the number of temperatures above .

071.e15.excalidraw.dark.svg

Exercise 16.

The ages are .

a) Draw a stem-and-leaf plot.

b) State the median.

c) State the range.

071.e16.excalidraw.dark.svg

Exercise 17.

A class records the times in minutes: .

a) Draw a stem-and-leaf plot.

b) State the mode.

c) State the largest time.

071.e17.excalidraw.dark.svg

Exercise 18.

The scores in a game are .

a) Draw a stem-and-leaf plot.

b) State the number of scores in the twenties.

c) State the median.

071.e18.excalidraw.dark.svg

Potential Misunderstandings

  • Students may confuse the stem with the leaf and reverse the digits
  • Students may not realise that each leaf represents a separate data value
  • Students may forget to order the leaves in ascending order
  • Students may join leaves together and treat them as one number instead of separate values
  • Students may read as instead of in this context
  • Students may place a value in the wrong stem because of weak place-value understanding
  • Students may think a stem-and-leaf plot only shows grouped data rather than the actual values
  • Students may make errors finding the median or range if they do not interpret the plot correctly

Next: 072e. Pie Charts and Divided Bar Graphs